robust progressive image transmission over ofdm systems...

394 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 4, NO. 3, SEPTEMBER 2002

Robust Progressive Image Transmission Over OFDMSystems Using Space-Time Block Code

Jie Song and K. J. Ray Liu, Senior Member, IEEE

Abstract—A joint source-channel coding (JSCC) scheme forrobust progressive image transmission over broadband wire-less channels using orthogonal frequency division multiplexing(OFDM) systems with spatial diversity is proposed for the ap-plication environments where no feedback channel is availablesuch as broadcasting services. Most of current research aboutJSCC focus on either binary symmetric channel (BSC) or additivewhite Gaussian noise (AWGN) channels. To deal with fadingchannels in most of previous methods, the fading channel ismodeled as two state Gilbert-Elliott channel model and the JSCCis normally aimed at the BER of bad channel status, which isnot optimal when channel is at good status. By using diversitytechniques and OFDM, the frequency selective fading effects inbroadband wireless channels can be significantly decreased andwe show that subchannels in OFDM systems approach Gaussiannoisy channels when the diversity gain gets large, as a result, thesystem performance can be improved in terms of throughput andchannel coding efficiency. After analyzing the channel property ofOFDM system with spatial diversity, a practical JSCC scheme forOFDM system is proposed. The simulation results are presentedfor transmit diversity with different number of antennas anddifferent multipath delay and Doppler spread. It is observed fromsimulations that the performance can be improved more than4 dB in terms of peak signal-to-noise ratio (PSNR) of receivedimageLena and the performance is not very sensitive to differentmultipath spread and Doppler frequency.

Index Terms—Image transmission, multimedia communica-tions, OFDM.

I. INTRODUCTION

T HE public’s desire for multimedia communications overbroadband wireless channels combined with the in-

creasing demands for Intranet access suggests a very promisingfuture for wireless data services. For multimedia communica-tions, the delay constraint limits the use of Automatic RepeatreQuest (ARQ), and in some cases the feedback channel is notavailable such as broadcasting service. The unequal importanceproperty and delay constraint of multimedia data suggests theuse of joint source-channel coding (JSCC) scheme which hasbeen studied in the last decade [1], [2], [4], [8]. The existingtechniques for JSCC can be divided roughly, into two main cat-egories: 1) the source and channel coding is combined togetherto minimize the total distortion incurred by source coding and

Manuscript received November 10, 1999; revised August 7, 2001. The asso-ciate editor coordinating the review of this paper and approving it for publicaitonwas Dr. Chung-Sheng Li.

J. Song is with the Agere Systems, Holmdel, NJ 07733 USA (e-mail:[email protected]).

K. J. R. Liu is with the Department of Electrical and Computer Engineering,Institute for System Research, University of Maryland, College Park, MD 20742USA (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TMM.2002.802845.

noisy channel (e.g., [4]). These can be regarded astrue jointsource-channel coding and 2) the source code is optimized fora noiseless channel, and is then made robust toward channelerrors by a optimal channel coding and/or modulation policy tominimize the channel errors while optimizing the throughput[2], [8]–[10], [12]. This kind of JSCC is of practical interestsbecause most of current image and video coding standards arebased on noiseless channel assumption. We denote this kindof method as joint source-channel matching (JSCM) as men-tioned in [9]. Most of the JSCM schemes focus on the binarysymmetric channel (BSC) or additive white Gaussian noise(AWGN) channel where the bit error rate or signal-to-noiseratio (SNR) is constant. To deal with fading channels in wirelesscommunications, the fading channel is modeled as two-stateGilbert-Elliot model and the JSCM normally aims at the BERof bad channel status [10], [14]. However, this scheme is notoptimal when channel is ingood condition. Another way isadaptive JSCM, where the channel state information (CSI) isavailable at the transmitter through a feedback channel. But inwireless communications it is normally impractical to get theCSI through feedback channel because of limited bandwidthof feedback channel, or there is no feedback channel availablesuch as in broadcasting services.

The transmission of the images coded using set partitioning inhierarchical trees (SPIHT) [26] across noisy channels is an ac-tive research topic recently. For example, in [8], a concatenatedchannel coding scheme was applied to SPIHT coded image toachieve performance gains over previous coding systems formemoryless channels with known statistics. In [11] and [12], aoptimal source and channel rate allocation scheme is proposedfor channels with and without feedback channel. A packeti-zation scheme in [13] was proposed that the output bitstreamof zerotrees encoder was reordered and packetized in such away that complete trees of wavelet coefficients were containedwithin packets. This allows graceful degradation of an image inthe presence of packet erasures, instead of loss of synchroniza-tion typically experienced with the error-sensitive zerotree en-coder. In [7], a product channel code structure is used to makethe system in [8] robust to fading channels. A combination ofchannel coding and packetization is proposed in [6], which canperform well on channels that can suffer packet losses as wellas statistically varying bit errors.

In this paper, a joint source-channel matching scheme forprogressive image transmission over broadband wireless chan-nels using OFDM systems with spatial diversity is proposed,where neither feedback channel nor CSI is available at trans-mitter. Multimedia transmission over asymmetric digital sub-scriber lines (ADSL) have been studied recently [5], [3], where

1520-9210/02$17.00 © 2002 IEEE

SONG AND LIU: ROBUST PROGRESSIVE IMAGE TRANSMISSION OVER OFDM SYSTEMS 395

Fig. 1. System structure for joint source–channel image transmission over OFDM channels using multiple antennas.

the channel is assumed to be time-invariant. For high bit-ratewireless communications, OFDM [16] is an attractive techniqueto be used because of its simplicity in dealing with frequency-se-lective, time-dispersive wireless fading channels [16], [19]. Di-versity techniques, including spatial, frequency, and time do-main diversity, have been suggested to decrease the fading ef-fect. Sufficiently spaced antennas are an attractive source of di-versity since they do not typically incur bandwidth expansionas in frequency division diversity, and does not incur delay as intime diversity. Though spatial diversity can be available at bothtransmitter and receiver, most of past work has focused on ex-ploiting receiver diversity since simple combining techniques,such as maximum ratio combining (MRC) or antenna selection,are available to obtain sufficient diversity gain [15]. However,it may not be possible to obtain much diversity gain at mobileterminal because of the space and power limitations at mobileterminals. A common technique to solve this problem is to usemultiple transmit antennas at base station to provide transmitdiversity. Some transmit diversity schemes have been proposedrecently such as delay diversity, space-time trellis coding [17],and space-time block coding [18], [20]. It should be noted thatour scheme focuses on broadband wireless communications,and, using spatial diversity to deal with fading effects which aredifferent from other proposed image transmission schemes, theproposed techniques can definitely be used in conjunction withall of these techniques as previously mentioned.

We consider using space–time block codes (STBC) as aspatial diversity technique to decrease the fading effects inboth time an frequency domain for OFDM systems, and showthat the subchannels in OFDM can be modeled as parallel flatRayleigh fading channels andindependent Gaussian noisychannels when the diversity gain goes to infinity. Then, aJSCM scheme for OFDM system with STBC is presented forSPIHT encoded image transmission, where the channel stateinformation is not available at the transmitter but known at thereceiver.

The remainder of the paper is organized as follows. In Sec-tion II, the system structure is described, then, in Section III, thechannel property of OFDM system with STBC is studied and

we show that the subchannels of OFDM system can be mod-eled as Gaussian noisy channels when the diversity gain is largeenough. In Section IV, a JSCM scheme is proposed for imagetransmission over OFDM system using STBC. In Section V,simulation results are presented under different diversity gainand fading parameters. Finally, conclusions are reached.

II. SYSTEM DESCRIPTION

The system structure is shown in Fig. 1. The image codingalgorithm used is SPIHT [26], which is a refined version ofthe Embedded Zerotree algorithm [25]. The output of SPIHTencoder is progressive, such that wherever the transmission isstopped, the received data can be used to reconstruct an imagewith corresponding quality. The SPIHT bitstream is packetizedinto source-packets of size bits for packet . Alinear block code (e.g., RS code or convolutional codewith known tail state) is used to protect source-packet. The re-sulted codewords are of equal size and treated as OFDM blocksto the transmitter. There are total of OFDM blocks, where

is decided by the transmission rate. The source-packet sizeis obtained by a JSCM algorithm to min-

imize the average distortion of the reconstructed image at thereceiver. The STBC with transmit antennas and receiverantennas is denoted as multiantenna system. The STBCfor two transmit antennas is proposed by Alamouti [20]. Tarokhet al.extended it to a general STBC by orthogonal design [17],[18]. The maximum-likelihood decoding can be achieved forSTBC based only on linear processing at the receiver. Alam-outi and Tarokhet al.have shown in [20] and [17] thatSTBC is equivalent to receiver diversity with max-imal ratio combining (MRC). This is an important result be-cause the performance analysis of STBC can be transfered toreceiver diversity with MRC which has been well studied. Themultipath Rayleigh fading channels between transmit antenna

and receive antenna is denotedas where is the total number of paths be-tween and . Each path is zero mean complex Gaussianprocess with variance , which are normalized such that


Fig. 2. Based-band OFDM system.

. All the ’s are statistically independent fromeach other for different and .

A. Orthogonal Frequency Division Multiplexing

The base-band OFDM system is shown in Fig. 2, whereare the transmitted symbols, is the channel impulse

response, is the white complex Gaussian channel noiseand are the received symbols. The ’s are taken from a

-ary signal constellation. The and converterscontain ideal low-pass filters with bandwidth , whereis the sampling interval. A cyclic extension of time lengthis used to eliminate inter-block interference and preserve theorthogonality of tones. The channel impulse responseis atime-limited pulse of the form

(1)

where is the number of paths between transmitter and re-ceiver; each path is complex Gaussian process with zero-meanand variance . The path delay satisfies , i.e., the en-tire impulse response lies inside the guard space. The channelresponse is normalized such that .

Using (1), the frequency response of the time-varying radiochannel at time is

(2)

For an OFDM system with block length and tone spacing(subchannel spacing) , the output signal after FFT at thethtone of the th OFDM block can be expressed as

(3)

where is additive Gaussian noise at theth tone andthe th block, with zero-mean and variance. We also as-sume is independent for different ’s, ’s.

is the frequency response at theth tone of theth block.

Fig. 3. Space-time block code for OFDM systems.

B. Space-Time Block Coding Scheme for OFDM

A simple transmit diversity for OFDM systems with twotransmit antennas is proposed in Fig. 3. In this paper, we use

multiple antenna system for simplicity. An OFDMblock is denoted as a complex vector , where is thediscrete time index for , with being the OFDMsymbol interval. There are complex subsymbols indenoted as , where is the totalnumber of subchannels in OFDM systems.

Assume there are two transmit antennas and two receive an-tennas. Two OFDM blocks and are collected fromthe output of signal mapper where each subsymbol is mappedto a point in a signal constellation set. For and ,the OFDM blocks for transmit antenna 0 and 1 after STBC en-coding are denoted as and ,respectively. For subchannel , the STBC en-coder works as follows:

(4)

where denotes complex conjugate.


The channel impulse response between transmit antennaandreceive antenna is

(5)

where is the delay of the th path between and . Thechannel frequency response at timeand subchannel is

(6)

Assume the channel state is constant over two OFDM symbolintervals, we have

(7)

where is the amplitude of , which is aRayleigh fading channel.

As a result, the received subsymbol at subchannelfrom re-ceiver antenna after FFT demodulation are

(4)

(4)

(8)

and the combiner for receive antenna is [20]

(9)

After combining the outputs of the two receive antenna 0 and 1,we have

(10)

Substituting (7)–(9) into (10), we get

(11)

The combined signals in (11) are then sent to the maximumlikelihood detector where for choose if andonly if

(12)

or for MPSK signals choose if and only if

(13)

where are points in a signal constellation set. Similarly,the decision rule can be used for subsymbol .

It is straightforward to implement receiver antennasto get more diversity gains [20]. It is shown in [20], [18] thatthe STBC scheme is equivalent to receiverdiversity using MRC.

III. CHANNEL PROPERTY OFOFDM SYSTEM USING

SPACE-TIME BLOCK CODE

By using OFDM, the whole bandwidth is divided into a largenumber of subchannels, where each subchannel is nonfrequencyselective and the intersymbol interference (ISI) can be neglectedwhen guard interval is inserted in each OFDM symbol. It isalready known that the subchannels in OFDM are flat Rayleighfading channels. Next, we study the property of OFDM systemwith STBC.

We know that the channel capacity of a bandwidth limitedGaussian noisy channel can be expressed as [21]

(14)

where SNR is the signal-to-noise ratio.The channel capacity for Rayleigh fading has to be calcu-

lated in an average sense because the SNR varies in time. In flatRayleigh fading environment, the signal model for-branchreceiver diversity is

(15)

where is zero-mean complex Gaussian variable with vari-ance 0.5 in each dimension, is the baseband transmittedsignal with signal energy is the additive white Gaussiannoise with variance at receiver antenna. Note that canalso be expressed as , then the MRC com-bines the received signal as

(16)

the instantaneous SNR at receiver at timeis [24]

(17)

and the average receiver SNRis

(18)


Let denote the probability density offor -fold receiverdiversity with average receiver SNR, then the average channelcapacity is [24]

(19)

and

(20)

The average channel capacity for AWGN and flat Rayleighfading channel with different is plotted in Fig. 7. It canbe noted that the channel capacity in the Rayleigh fading for

and greater is very close to that in the Gaussian noiseenvironment.

Several points can be summarized as follows [22].

1) The channel capacity in a Rayleigh fading is in an averagesense.

2) The channel capacity in a Rayleigh fading is always lowerthan that of a Gaussian noise channel.

3) The diversity scheme can increase the channel capacity ina Rayleigh fading environment.

When the diversity gain increases, we have the followingproposition.

Proposition 1: When the number of diversity branches, the channel capacity of a -branch signal in a

Rayleigh fading environment approaches the channel capacityin a Gaussian noise environment.

Proof: From (18), the transmitted signal energyfor agiven average receiver SNRis

(21)

From (17), the instantaneous SNR at receiver with an-tennas is

(22)

From the Law of Large Numbers [23], we have

(23)

then the channel capacity at timeis

(24)

Now we have the following conclusion.Proposition 2: When OFDM system with

space-time block code is used in a frequency-selective,time-dispersive Rayleigh fading environment, the frequencyresponse of OFDM subchannels can be modeled as parallel,independent Gaussian noisy channels when .

Proof: We know that the subchannels in OFDM are par-allel flat Rayleigh fading channels. It is also shown that a sub-channel in OFDM system with space-time block codeis equivalent to receiver diversity system with MRC.Furthermore, it is proved in Proposition 1 that a flat Rayleigh

fading channel with -branch receiver diversity approachesGaussian noisy channel when . Then when ,the conclusion is reached.

IV. JOINT SOURCE–CHANNEL MATCHING

FOR OFDM USING STBC

Now we consider the joint source-channel matching schemefor progressive image transmission over OFDM systems using

STBC. First, we derive a JSCM method for OFDMsystems with STBC with the assumption that the OFDM sub-channels are parallel, independent Gaussian noisy channels withthe same SNR. For OFDM systems with finite antennaSTBC, we propose to usetargetSNR to satisfy the assumptionbased on which the JSCM is proposed. We assume the averageSNR is known at both transmitter and receiver.

A. Joint Source-Channel Matching Scheme for OFDM Systems

The problem considered is as follows. The SPIHT encodedbitstream is to be transmitted over OFDM systems using

STBC. The transmission rate is bit-per-pixel (bpp).There are subchannels in the OFDM and each subchannelis modulated by a complex symbol from a-ary modulationset, e.g., QPSK. The SPIHT stream is packetized intosource-packets with bits for packet , where

is the total number of OFDM blocks decided by . Forchannel coding, we assume that we are provided with a finitenumber of block code. These channel codes operate on sourcepackets which are CRC-16 outer coded first, here we use theterms that are used in the concatenated code, CRC is outer codeand RS is inner code. The resulted blocks of codeword are ofequal size and are subsequently transmitted over the channelsas OFDM blocks. The total number of OFDM blocksusedfor transmission should satisfy

(25)

where and is the dimension of the image, is theconstellation size for subchannels.

The source packets are channel-coded by the assignedchannels codes and transmitted over the noisy channel. Thereceiver tries to recover the source-packets from the noisyreceived OFDM blocks. The channel decoder either correctlydecodes a source-packet or detects an error. We assume thatthe probability of undetected error is zero because of CRC-16error detection. For SPIHT bitstream, if a packet cannot bedecoded correctly then the subsequent packets cannot be usedto improved the quality of the source. Hence, at the receiver,the source is reconstructed only from the decoded bit-streamup to the first packet that is error-detected.

RS channel code is used here because of its bursty error cor-rection capability. It should be pointed out that other channelcodes combined with interleaver could also be used to havebetter performance. Our objective is to show that JSCM basedon spatial diversity is an alternative solution for wireless multi-media communications where delay constraint and performancecould be satisfied without interleaver and ARQ. Each OFDMblock is a RS codeword over , where


is the total number of RS code sym-bols in each OFDM block, and is the number ofRS information symbols in OFDM block . Wedenote the error-correction failure probability of OFDM block

as .

If the first source-packets are correctly received, the imagecan be reconstructed to a ratebpp. If the peak-signal-to-noise-ratio (PSNR) function of thesource coder for the image is given by , then theJSCM algorithm is to look for a source packetization scheme

, which specifies the sequence of source-packet size asto maximize the expected PSNR of

the reconstructed image [10], [9]

(26)

It is difficult to use (26) in practice because thefunction is not available at both transmitter and receiver, or ahigh quality channel is required to transmit the sideinformation from transmitter to receiver. An alternative criteriais to use the expected number of source bits correctly receivedas suggested in [12] where dynamic programming is used tosolve the optimization problem similar to (26). Even though theuse of the number of received bits is not as precise as using

or rate-distortion function , it was shown in[28] that the performance of using expected received bits is al-most as good as using PSNR or rate-distortion function. Themajor difference between the JSCM we proposed here and theothers is that, in our scheme, the channel codewords are of equallength, and we look for the length of source packet in each code-word such that the average distortion at receiver is minimized.We call this scheme variable source-packet length (VSL) JSCMto distinguish the equal source-packet length (ESL) algorithmused in most of current literatures where the source-packets areof equal length. The VSL method is more suitable than ESLhere because the length of the codewords is limited in block datatransmission scheme for OFDM and RS block codes.

If the average number of source bits received before errorsoccur is used to find the source-packet packetization schemefor a given , it can be written as

(27)

This optimization problem can be solved by dynamic program-ming as proposed in [12]. For integers and apacketization scheme, define

(28)

then we have the recursive relation for dynamic programming

(29)

Now the optimization problem in (27) becomes

(30)

The optimization solution is usedto packetize the SPIHT bitstream and protected byover .

B. Compute the Error Probability of OFDM Block

The decoding failure probability of a OFDM blockover under the assumption of mutual

independence of OFDM subchannels is [27]

(31)

where is the error probability of RS code symbol (bits perRS code symbol), which is

(32)

where is the number of bits for each subchannel symbol, andis the number of subchannel symbols in a RS code symbol.

e.g., for QPSK and .All the computations in (31) and (32) are based on the as-

sumption that the subchannels in OFDM with STBC aremutually independent Gaussian noisy channels with the sameSNR, which is true when goes to infinity. For finite ofSTBC , the assumption doesn’t hold. Also, the instanta-neous SNR at receiver, denoted as, is time-varying. Becausethe transmitter cannot know the, the JSCM scheme has to bedesigned for a single SNR, which we calltarget SNRand denoteas . The target SNR is computed for a given probability

such that . By specifying a relativelysmall , the is larger than with high probability andthe system performance can be guaranteed. We call this schemeworst-case JSCM design. The advantage of using STBC or spa-tial diversity is that thetarget SNR approaches the averageSNR as the increases. As a result, the system performancecan be improved.

For a OFDM system using STBC, the instant SNRat subchannels with a known average receiver SNRis

(33)


Fig. 4. The CDF of diversity gains for receiver diversity usingM antennas.

TABLE ITHE TARGETSNRFOR AVERAGE RECEIVERSNR = 1 AT DIFFERENTP

UNDER DIFFERENT(N;M) STBC CASES

where is the amplitude of complex zero-mean Gaussianrandom variable with variance 0.5 at each dimension. Let

, then is a random variable with-degree freedom. To find thetarget SNR such that

for a given , we only need to find a realvalue such that , then using (33) we have

(34)

The cumulative distribution function (CDF) ofis [24]

(35)

where the CDF of is shown in Fig. 4 for different s. Itshows that the fading effect can be significantly decreased as

increases. To show the advantage of using diversity, thefor different STBC at same average receiver SNR

is listed in Table I for several ’s. Indeed, as, which follows the Proposition 1.

After the target SNR is obtained, theworst-casesub-channel symbol error probability of Gray-mapped QPSK is[24]

(36)

For other MPSK symbols except BPSK and QPSK, has tobe obtained numerically for a given .

In general, the scheme for robust progressive image transmis-sion over OFDM systems with STBC is summarized asfollows.

Fig. 5. Partition and group method for substreams of wavelet coefficients.

1) Given the system parameters:number of subchannels in OFDM;number of OFDM blocks will be transmitted;average SNR at receiver;number of transmit antennas and receive antennas;RS channel code is based on , or bits perchannel code symbol;number of bits for each subchannel symbol.

2) Thetarget SNR is computed for a specified using(34).

3) Compute the BER and subchannel symbol error rate(SER) using (36).

4) Compute the RS code symbol SER and OFDM block de-coding failure probability using (32) and (31).

5) Find the source-packet packetization schemeby solving (27). The obtained vari-

able source-packet lengths are known by both transmitterand receiver through a reliable control channel.

6) The SPIHT bitstream is packetized intoblocks withbits for block which is CRC-16

outer coded, then RS inner coded using overto form a OFDM block.

7) The OFDM blocks is space-time coded and transmittedas described in Section II-B.

The receiver performs the same computation as given aboveto get the size of source-packet for the givenparameters. Then, after demodulation and RS decoding, the re-ceiver uses the CRC-16 to detect the first error source-packet ifany, and reconstructs the image using SPIHT decoder.

V. SIMULATION RESULTS

In our simulation, we use a two-ray channel model with delayspread from 0 to 40s and Doppler frequency from 10 Hz to 200Hz. Two transmit antennas and receive antennas areused for space-time block code. The entire channel bandwidth,800 kHz, is divided into 128 subchannels. Four subchannels oneach end are used as guard tones and the rest 120 tones are used


Fig. 6. Structure of SPIHT for substreams.

Fig. 7. The spectral capacity density per unit time on the Rayleigh fadingchannel,M -fold diversity channels(M = 2; 4; 8) and the AWGN channel.

to transmit data. To make the tones orthogonal to each other, thesymbol duration is 160 s. An additional 40 s guard intervalis used to provide protection from ISI due to channel multipathdelay spread. This results in a total block length sand a subchannel symbol rate kBd. QPSK modula-tion and coherent estimation is used with the assumption ofperfect channel information at receivers. The punctured and/orshortened RS code over is used such that each OFDMblock has RS code symbols, and the numberof information symbols in each OFDM block is in the range

Fig. 8. The transmission order for MDC SPIHT substreams.

Fig. 9. PSNR comparison between MDC-SPIHT and SDC-SPIHT at (2, 4)and (2, 2) STBC,f = 20 Hz, � = 10 �s,P = 0:01.

. In all the simulations, 300 times image trans-mission are simulated under each case. The transmit rate usedfor all the simulations is 0.5 bpp, which is approximately equiv-alent to OFDM blocks.

A. Performance Comparisons

The discrete wavelet transform of gray imageLena is obtained first, then two schemes are compared for givensystem parameters.

1) Single stream transmission (SDC-SPIHT):The DWTcoefficients is encoded into a SPIHT bitstream, and ispacketized into packets withbits for packet . The packetization scheme is obtainedthrough the JSCM scheme described above. Then thesource-packets are CRC-16 outer coded and RS innercoded to form OFDM blocks and sent out through STBCencoder.




2) Multiple substream transmission (MDC-SPIHT):TheDWT coefficients are partitioned into subimages,and each subimage keeps the tree structure across scalesas shown in Fig. 5, then each subimage is SPIHT codedas shown in Fig. 6. It was shown in [29], [30] that thepartition of the coefficients into subimage is robust tobits and packet error in noisy channels. Each SPIHT sub-stream is packetized into ,which is obtained through the JSCM scheme forblocks. Then the source packetis CRC-16 outer codedand inner coded to form a OFDM block.The OFDM blocks is transmitted across the substreamsas shown in Fig. 8 such that the OFDM blocks withinone substream are interleaved while the progressivetransmission property is still maintained with a delayof OFDM blocks. In the simulation the number ofsubimage used is 16.


Fig. 13. Packetization scheme comparison between MDC-SPIHT andSDC-SPIHT at (2, 4) STBC, where packetization for MDC-SPIHT is based on36 OFDM blocks, SDC-SPIHT is based on 576 OFDM blocks.

In Figs. 9–12, the average PSNR of the received images iscompared with using STBC (2, 4) and (2, 2), underdifferent delay spread and Doppler spread parameters. It canbe observed that at the same average received SNR, the imagequality using STBC (2, 4) is always better than using STBC (2,2) because thetarget SNRof STBC (2, 4) is larger than that ofSTBC (2, 2), as a result, the JSCM scheme has larger throughputfor STBC (2, 4) than that of STBC (2, 2). Also, when the diver-sity gain is increased, the subchannels in OFDM systemapproaches Gaussian noisy channel, which is the assumption onwhich the JSCM algorithm is based.

We can also note that the performance of MDC-SPIHT isbetter than that of SDC-SPIHT at moderate average SNR, thisis because of the following two reasons.

• In SDC-SPIHT, when one source-packet is error-detected,then all the source-packets followed can not be used; In


Fig. 14. Performance comparison at different multipath delay spread and Doppler frequency: (a) SDC-SPIHT with STBC(2, 2), (b) MDC-SPIHT with STBC(2,2), (c) SDC-SPIHT with STBC(2, 4), and (d) MDC-SPIHT with STBC(2,4).

MDC-SPIHT, however, the error of one source-packetonly affect the source-packets followed in that single sub-stream. The interpolation from the neighbor coefficientsat Subband from other substreams can be used toconceal the error effects.

• The effective source-rate of MDC-SPIHT is larger thanthe source-rate of SDC-SPIHT in most cases. For a giventransmission rate , the corresponding source rate forMDC-SPIHT is

(37)

and for SDC-SPIHT is

(38)

For a given average SNR, the packetization scheme for oneMDC-SPIHT substream (36 OFDM blocks) is the same asthe last 36 OFDM blocks in SDC-SPIHT. For example, thesource-packetization scheme obtained whendB for both MDC-SPIHT and SDC-SPIHT is shown inFig. 13. Because of the progressive property of SPIHT

bitstream, we know that , for , then wehave , as a result,

.On the other hand, when the SNR is large enough, the

throughput limit is reached such that . ThenSDC-SPIHT has better performance than MDC-SPIHT be-cause the source coding efficiency of SDC-SPIHT is betterthan MDC-SPIHT.

The performance under different multipath delay spread andDoppler frequency for same STBC configuration are also com-pared. The average PSNR of SDC-SPIHT and MDC-SPIHTat different delay spread and Doppler spread is shown inFig. 14(a)–(b) using STBC (2, 2). The same comparison forSTBC (2, 4) is also shown in Fig. 14(c)–(d). We can see thatthe multipath delay spread and Doppler spread have less effectsto the performance when the diversity gain increases.Actually, when , the system performances are almostthe same under different multipath delay and Doppler spreadbecause the OFDM subchannels approach Gaussian noisychannels.

The received images of “Lena” is also shown in Fig. 15,when dB, where the delay spread s,Doppler frequency Hz. The probability fortarget SNR


(a) PSNR= 25.72 dB (b) PSNR= 27.12 dB

(c) PSNR= 31.24 dB (d) PSNR= 33.59dB

Fig. 15. Received images of “Lena” whenE =N = 9 dB at (a) SDC-SPIHT with STBC(2, 2), (b) MDC-SPIHT with STBC(2, 2), (c) SDC-SPIHT with STBC(2,4), and (d) MDC-SPIHT with STBC(2, 4). Doppler frequencyf = 200 Hz, multipath delay� = 40 �s,P = 1% for JSCM.

% is used in JSCM algorithm. At the same STBC config-urations [(2, 4) or (2, 2)], MDC-SPIHT has better image quality(Fig. 15(b) and (d)) than that of SDC-SPIHT [Fig. 15(a) and(d)], respectively. The image quality of STBC (2, 4) as shownin Fig. 15(c) and (d) is much better than the image quality ofSTBC (2, 2) as shown in Fig. 15(a) and (b).

B. Error Propagation and Concealment

Even though the fading effects can be decreased significantly,the errors may still occur and propagate. Fig. 16(a) shows a

sample of channel gain of OFDM channels with one transmitterand one receiver over two-ray fading channels. Fig. 16(b) showsa sample of channel gain with two transmitter and four receiverswith the same average SNR. It can be noted that the dynamicrange of Fig. 16(b) is much smaller than Fig. 16(a) because ofusing multiple antennas. To illustrate the error propagation andconcealment effects, we assume that one of the 16 substreams islost. Fig. 17(a) shows the decoded image when one of the sub-stream is lost and the corresponding coefficients are replaced byzero. The decoded image has dark “holes” spread out to an ex-tent determined by the number of decomposition levels and the


Fig. 16. Channel gains using two-ray Rayleigh fading channel model: (a) one transmitter and one receiver and (b) two transmitters and four receivers.

(a) (b)

Fig. 17. The reconstructed images using MDC when one substream is lost: (a) without error concealment (the lost coefficients are replaced by zero) and(b) Withsimple error concealment. (The lost low frequency coefficients are replaced by interpolation from neighboring coefficients.)

filter length. To conceal the lost coefficients, we simply sub-stitute low-frequency coefficients of the lost coefficients by theaverage of the neighboring correctly received coefficients. Thecorresponding high-frequency coefficients are still replaced byzero. Fig. 17(b) shows the recovered image using the simpleconcealment method. It can be noticed that the image quality isimproved significantly at smooth area. However, there is blur-ring in synthesized edges since high frequency coefficients arenot recovered. Advanced image reconstruction techniques, suchas in [31], can be employed to improve the quality by recov-ering both low frequency and high frequency coefficients usingdifferent schemes.

VI. CONCLUSION

A joint source–channel matching framework is proposed forSPIHT coded image transmission over OFDM systems withmultiple antennas using space–time block code. By using spa-tial diversity, the fading effect of wireless channels can be sig-nificantly decreased. After showing that the OFDM subchan-nels are indeed parallel independent Gaussian noisy channel

in a frequency-selective, time-dispersive Rayleigh fading envi-ronment when the number of antennas goes to infinity, a jointsource–channel matching scheme is proposed for OFDM sys-tems using multiple antennas. The simulation results show thatthe performance is improved significantly in terms of image ratethroughput and channel coding efficiency. To further decreasethe channel impairment, we use an error resilient SPIHT imagecoding algorithm to divide the image into several subimages,where the proposed joint source–channel matching scheme canbe applied directly to each SPIHT encoded subimage. By doingso, the error propagation is only constrained within one sub-stream and error concealment techniques can be employed toachieve better reconstruction at the receiver. The simulation re-sults show that this scheme is robust to different Doppler andmultipath delay spread in wireless communications.

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Jie Songreceived the B.S. degree from Beijing Uni-versity, Beijing, China, in 1990, the M.S. degree fromBeijing University of Posts and Telecommunications(BUPT) in 1993, and the Ph.D. degree from Univer-sity of Maryland, College Park, in 2000, all in elec-trical engineering.

From 1993 to 1996, he was a Lecturer andResearcher, Information Engineering Departmentat BUPT. From 1997 to 1999, he was a part-timeconsultant of multimedia technologies with OdysseyTechnologies, Inc., Jessup, MD, where he was

involved in the projects of H.323/H.324 videophone, portable multimediaterminal design, and multichannel video capturing systems. Since 2000, hehas been working on research, design, and implementation for broadbandcommunication systems with the Microelectronics group, Lucent Technologies(now Agere Systems), Holmdel, NJ. His research interests include signalprocessing for digital communications and multimedia communications.

K. J. Ray Liu (SM’93) received the B.S. degreefrom the National Taiwan University, Taipei, Taiwan,R.O.C., and the Ph.D. degree from the Universityof California, Los Angeles, both in electricalengineering.

He is a Professor with the Electrical and ComputerEngineering Department and Institute for SystemsResearch, University of Maryland at College Park.He was a Visiting Professor at Stanford University,Stanford, CA, Information Technology University,Copenhaven, Denmark, and Hong Kong Polytechnic

University. His research interests span broad aspects of signal processingalgorithms and architectures, image/video coding, compression and processing,wireless communications, security, and biomedical and medical technology. Hehas published over 250 papers, of which over 75 are refereed journal papers.He is Editor-in-Chief ofEURASIP Journal on Applied Signal Processing, aneditor of theJournal of VLSI Signal Processing Systemsand the series editorof the Marcel Dekker series on signal processing and communications.

Dr. Liu has received numerous awards , including the 1994 National Sci-ence Foundation Young Investigator Award, the IEEE Signal Processing So-ciety’s 1993 Senior Award (Best Paper Award), the IEEE Vehicular TechnologyConference (VTC) 1999 Best Paper Award, Amsterdam, The NEtherlands, theGeorge Corcoran Award in 1994 for outstanding contributions to electrical en-gineering education and the 1995–96 Outstanding Systems Engineering FacultyAward in recognition of outstanding contributions in interdisciplinary research,both from the University of Maryland, and many others. He is has been an As-sociate Editor of IEEE TRANSACTIONS ONSIGNAL PROCESSING, a Guest Editorof special issues on Multimedia Signal Processing of the PROCEEDINGS OF THE

IEEE, a Guest Editor of special issue on Signal Processing for Wireless Com-munications of IEEE JOURNAL OF SELECTED AREAS IN COMMUNICATIONS, aGuest Editor of special issue on Multimedia Communications over Networks ofIEEE SIGNAL PROCESSINGMAGAZINE, a Guest Editor of special issue on Mul-timedia over IP of IEEE TRANSACTIONS ONMULTIMEDIA . He currently servesas the Chair of Multimedia Signal Processing Technical Committee of the IEEESignal Processing Society.

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